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受欢迎的代数 >

5nx^4(1/5)^3=125

解答

5 n x^{4} (\frac{1}{5})^{3} = 125

解答

x = \frac{5 4 5}{n}, x = - \frac{5 4 5}{n}, x = i \frac{5 4 5 n ^{\frac{3}{4}}}{n}, x = - i \frac{5 4 5 n ^{\frac{3}{4}}}{n}

求解步骤

5 n x^{4} (\frac{1}{5})^{3} = 125

两边除以

5 n (\frac{1}{5})^{3}; n \neq = 0

x^{4} = \frac{3125}{n}; n \neq = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = \frac{3125}{n}

解

u^{2} = \frac{3125}{n} : u = \frac{3125}{n}, u = - \frac{3125}{n}

u = \frac{3125}{n}, u = - \frac{3125}{n}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{3125}{n} : x = \frac{5 4 5}{n}, x = - \frac{5 4 5}{n}

解

x^{2} = - \frac{3125}{n} : x = i \frac{5 4 5 n ^{\frac{3}{4}}}{n}, x = - i \frac{5 4 5 n ^{\frac{3}{4}}}{n}

解为

x = \frac{5 4 5}{n}, x = - \frac{5 4 5}{n}, x = i \frac{5 4 5 n ^{\frac{3}{4}}}{n}, x = - i \frac{5 4 5 n ^{\frac{3}{4}}}{n}

作图

流行的例子

4x^4+x-3=5x^5+x-6

4 x^{4} + x - 3 = 5 x^{5} + x - 6

4 x + 8 = 6 x^{5} - 4

x^{4} - 4 x^{2} + 32 = 0

(d^{2} + 1)^{3} = 0

(x+5)^3=(-64)/(125)

(x + 5)^{3} = \frac{- 64}{125}